Installing toolboxes and setting up the path.

You need to unzip these toolboxes in your working directory, so that you have toolbox_signal and toolbox_general in your directory.

For Scilab user: you must replace the Matlab comment '%' by its Scilab counterpart '//'.

Recommandation: You should create a text file named for instance numericaltour.sce (in Scilab) or numericaltour.m (in Matlab) to write all the Scilab/Matlab command you want to execute. Then, simply run exec('numericaltour.sce'); (in Scilab) or numericaltour; (in Matlab) to run the commands.

We can display an isosurface of the dataset (here we sub-sample to speed up the computation).

sel = 1:2:n;
clf;
isosurface( M(sel,sel,sel), .5);
axis('off');

3D Tomograpic Measurements

Tomographic measurements corresponds to the computation of orthogonal projections (integration along liners) of the 3D datasets
on set of 2D planes. Thanks to the Fourier-slice theorem, this is equivalent to performing a sub-sampling of the 3D Fourier
transform along planes (orthogonal to the projection directions).

Number of projections

P = 12;

Either uniform sampling for P==12, or randomized projection directions, on the sphere.

The transposed operator corresponds to the pseudo inverse reconstruction (because the measurement operator is in fact an orthogonal
projection). It is similar to the filtered back-projection (excepted that the Fourier sub-sampling is now on a discrete grid,
which is not really faithful to the geometry of tomographic acquisition).